Iran's president-elect, Hassan Rouhani, whose sensational victory in Friday's election prompted nationwide celebrations, has promised to reduce tensions with the west, show more transparency on its nuclear front and bring moderation back to the forefront of Iranian politics.

In his first press conference in Tehran, two days after being confirmed as the elected successor to Mahmoud Ahmadinejad, Rouhani presented himself as a moderate politician willing to "enhance mutual trust" between Tehran and the international community, including Britain and the US, and as the saviour of the Iranian economy by working to lift sanctions.

"We have to enhance mutual trust between Iran and other countries," said Rouhani, nicknamed in the Iranian media as the diplomat sheikh and the sheikh of hope. "We have to build trust," he said. Rouhani made clear that his government will pursue a "friendly relationship" with all its neighbours, including the Arab countries, in particular Saudi Arabia.

The press conference, held in Iran's centre for strategic studies, an institution Rouhani has presided over for 22 years, was at times chaotic, as only a limited number of Iranian and foreign reporters in the packed room were given the chance to ask questions. The session, which lasted an hour and half, was broadcast live on national television.

In a sharp contrast to the outgoing president, Rouhani avoided issuing inflammatory statements against the west and instead promised improved relations. He outlined his priorities by saying: "Your government … will follow up national goals … in the path of saving the country's economy, revive ethics and constructive interaction with the world through moderation."

In regards to Iran's nuclear programme – which the west suspects to have military dimensions, while Tehran insists it is entirely for peaceful purposes – Rouhani said his government would restore "mutual confidence" by promoting step-by-step measures in order to reassure the international community about Iranian ambitions.

"The first step will be showing greater transparency," he said. "We are ready to show greater transparency and make clear that the Islamic Republic of Iran's actions are totally within international frameworks."

He described western sanctions targeting Iran's economy and its banking system as "cruel" and said his government's goal would be that no new sanctions are imposed and the existing measures are lifted.

"The Iranian nation has done nothing to deserve sanctions. The works it has done has been within international frameworks. If sanctions have any benefits, it will only benefit Israel. It has no benefits for others," he said.

Iran's national currency was sent into a tailspin last year as the toughest-ever sanctions imposed on Tehran since the 1979 Islamic republic started to have an impact. A serious shortage of medicine followed as banking restrictions impacted pharmaceutical companies in Iran and hundreds of thousands of Iranians with serious illness were put at risk.

Israel's prime minister, Benjamin Netanyahu, said in an interview on Monday that he did not think Rouhani could soothe nuclear tensions because Tehran's nuclear policies rested in the hands of Iran's supreme leader, Ayatollah Ali Khamenei.

"The Iranian election clearly reflects deep disaffection of the Iranian people with its regime, but unfortunately it doesn't have the power to change Iran's nuclear ambitions," Netanyahu said.

Despite the hostility among Iranian hardliners towards British media, a BBC journalist was allowed to ask a question about Tehran-London ties, which were downgraded in 2011 following the storming of the British embassy by angry protesters.

"We will try to improve relations with all countries we recognise based on mutual respect and the UK is not an exception," Rouhani said, signalling that diplomatic relations could be normalised.

UK foreign secretary William Hague said: "The government hopes that following Dr Rouhani's election, the Iranian government will take up the opportunity of a new relationship with the international community by making every effort to reach a negotiated settlement on the nuclear issue."

When asked by a US journalist if his mandate would included engaging in direct talks with the US, Rouhani said it was a difficult question but signalled it was possible, provided that the US government recognised the rights of Iranian people.

"The issue of relations between Iran and America is a complicated and difficult issue," Rohani said. "It is an old wound that needs to be healed."

Speaking on Syria, where the west sees Iran as complicit with Syria's Bashar al-Assad regime, Rouhani said his government would be opposed to foreign intervention. "It's up to the Syrian people to decide for their future," he said. "We are opposed to terrorism, civil war and foreign intervention and we hope peace and tranquillity will return to Syria through the cooperation with countries of the region and world."

Rouhani's victory was met with cautious optimism in the west, with the White House congratulating Iranians on their choice. Following his win, Tehran's stock exchange index has gone up and the national currency, the rial, recovered its value against the dollar. Web users also said internet speed has improved, with the restoration of access to VPNs used to bypass filtering and less jamming of satellite signals by the state.

Although the Iranian questions were focused mainly on the economy, the president was also pressed on the issues of political openness and press freedom. In an apparent reference to the house arrest of opposition leaders Mir Hossein Mousavi and Mehdi Karroubi, a journalist asked if he would work to lift restrictions on "leading political figures who have held key positions after the revolution". Rouhani responded saying it was not only his decision. At the end of the conference, one person shouted: "Rouhani remember, Mir Hossein should also be here." One commentator noted it was the first time Mousavi's name had been heard on national television for a long time and another wondered if he was watching the press conference in his house surrounded by security officials.